DeepAI
Log In Sign Up

Stochastic Learning Approach to Binary Optimization for Optimal Design of Experiments

01/15/2021
by   Ahmed Attia, et al.
0

We present a novel stochastic approach to binary optimization for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the regularized optimality criterion, is cast into a stochastic objective function in the form of an expectation over a multivariate Bernoulli distribution. The probabilistic objective is then solved by using a stochastic optimization routine to find an optimal observational policy. The proposed approach is analyzed from an optimization perspective and also from a machine learning perspective with correspondence to policy gradient reinforcement learning. The approach is demonstrated numerically by using an idealized two-dimensional Bayesian linear inverse problem, and validated by extensive numerical experiments carried out for sensor placement in a parameter identification setup.

READ FULL TEXT
06/10/2019

Randomization and reweighted ℓ_1-minimization for A-optimal design of linear inverse problems

We consider optimal design of PDE-based Bayesian linear inverse problems...
07/28/2020

Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations

Optimal experimental design (OED) is the general formalism of sensor pla...
08/10/2020

Optimal Bayesian experimental design for subsurface flow problems

Optimal Bayesian design techniques provide an estimate for the best para...
06/08/2019

Optimal Convergence for Stochastic Optimization with Multiple Expectation Constraints

In this paper, we focus on the problem of stochastic optimization where ...
12/18/2019

Optimal experimental design under irreducible uncertainty for inverse problems governed by PDEs

We present a method for computing A-optimal sensor placements for infini...